Transforming metrology data from a semiconductor treatment system using multivariate analysis

ABSTRACT

Metrology data from a semiconductor treatment system is transformed using multivariate analysis. In particular, a set of metrology data measured or simulated for one or more substrates treated using the treatment system is obtained. One or more essential variables for the obtained set of metrology data is determined using multivariate analysis. A first metrology data measured or simulated for one or more substrates treated using the treatment system is obtained. The first obtained metrology data is not one of the metrology data in the set of metrology data earlier obtained. The first metrology data is transformed into a second metrology data using the one or more of the determined essential variables.

BACKGROUND

1. Field

The present application relates to transforming metrology data from asemiconductor treatment system, and, more particularly, to transformingmetrology data using multivariate analysis.

2. Related Art

In semiconductor manufacturing, metrology is increasingly utilized toensure that individual process steps, as well as a sequence of processsteps, adhere to design specifications. For example, metrology may beemployed to identify instances of process drift, and provide datasufficient to establish control schemes for correcting such drift.

While critical dimension scanning electron microscopy (CD-SEM) metrologyhas been used in the past, the complexity of devices formed onsemiconductor substrates and their ever-decreasing feature size (e.g.,sub 100 nm technology nodes), coupled with increasingly sophisticatedunit process and process integration schemes, have warranted theimplementation of optical metrology. In addition to beingnon-destructive, in-line optical metrology, such as opticalscatterometry, can be used for robust Advanced Process Control (APC).

In optical scatterometry, one application includes the use of periodicstructures that are formed on semiconductor substrates in closeproximity to the locations for the formation of operating structures insemiconductor devices. By determining the profile of the periodicstructures, the quality of the fabrication process utilized to form theperiodic structures, and by extension the operating structure of thesemiconductor device proximate the periodic structures, can beevaluated.

In general, optical scatterometry involves illuminating the periodicgrating with electromagnetic (EM) radiation, and measuring the resultingdiffracted signal. The characteristics of the measured diffractionsignal is typically compared to a library of pre-determined diffractionsignals (i.e., simulated diffraction signals) that are associated withknown profiles. When a match is made between the measured diffractionsignal and one of the simulated diffraction signals, then the profileassociated with the matching hypothetical diffraction signal is presumedto represent the profile of the periodic grating.

However, the process of generating a simulated diffraction signaltypically involves performing a large number of complex calculations,which can be time consuming and computationally intensive. The amount oftime and computational capability and capacity needed to generatesimulated diffraction signals can limit the size and resolution (i.e.,the number of entries and the increment between entries) of the libraryof simulated diffraction signals that can be generated. Moreover, thecomplexity of the measured diffraction signals (i.e., the amount ofdata) and the potential for the existence of noise can further hinderaccurate correlation between measured diffraction signals and simulateddiffraction signals. For example, differences in measured diffractionsignals can often consist merely of a slight shift or small change inthe shape of broad spectral features in the measured diffractionsignals.

SUMMARY

In one exemplary embodiment, metrology data from a semiconductortreatment system is transformed using multivariate analysis. Inparticular, a set of metrology data measured or simulated for one ormore substrates treated using the treatment system is obtained. One ormore essential variables for the obtained set of metrology data isdetermined using multivariate analysis. A first metrology data measuredor simulated for one or more substrates treated using the treatmentsystem is obtained. The first obtained metrology data is not one of themetrology data in the set of metrology data earlier obtained. The firstmetrology data is transformed into a second metrology data using the oneor more of the determined essential variables.

DESCRIPTION OF DRAWING FIGURES

The present application can be best understood by reference to thefollowing description taken in conjunction with the accompanying drawingfigures, in which like parts may be referred to by like numerals:

FIG. 1 depicts a schematic view of a processing system according to anembodiment;

FIG. 2 depicts a schematic view of a structure formed on a substrateaccording to an embodiment;

FIG. 3 presents in schematic view a technique for illuminating astructure on a substrate with electromagnetic radiation according to anembodiment;

FIG. 4 illustrates an exemplary measured signal obtained fromilluminating a structure on a substrate with electromagnetic radiationaccording to another embodiment;

FIG. 5 illustrates exemplary essential variables (EV) for a plurality ofmeasured signals according to an embodiment;

FIG. 6 illustrates exemplary statistical properties for essentialvariables according to another embodiment;

FIG. 7A illustrates exemplary process performance parameter data as afunction of two controllable process parameters for a treatment processaccording to another embodiment;

FIG. 7B illustrates exemplary essential variable data as a function oftwo controllable process parameters for a treatment process according toanother embodiment;

FIG. 8A illustrates an contour plot of exemplary process performanceparameter data as a function of two controllable process parameters fora treatment process according to another embodiment;

FIG. 8B illustrates an contour plot of exemplary essential variable dataas a function of two controllable process parameters for a treatmentprocess according to another embodiment;

FIG. 9 illustrates a method of determining one or more essentialvariables according to another embodiment;

FIG. 10 illustrates a method of operating a treatment system utilizingone or more essential variables according to yet another embodiment; and

FIG. 11 depicts a schematic view of a processing system according to yetanother embodiment.

DETAILED DESCRIPTION

The following description sets forth numerous specific configurations,parameters, and the like. It should be recognized, however, that suchdescription is not intended as a limitation on the scope of the presentinvention, but is instead provided as a description of exemplaryembodiments.

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views, FIG. 1illustrates a material processing system 1 comprising a semiconductortreatment system 10 configured to treat a substrate, a processcontroller 12 for performing at least one of monitoring, measuring,adjusting, or controlling, or a combination of two or more thereof,process data for performing a treatment process in treatment system 10.Process data include values of process variables in the treatmentprocess such temperature and time for a treatment process. Materialprocessing system 1 further comprises a metrology system 14 formeasuring metrology data from one or more substrates resulting from thetreatment process performed in treatment system 10, and a data processor20. Metrology data includes measurement values of metrology instrumentssuch as scatterometers, CDSEMs, and the like. The process controller 12is capable of executing the method of performing the treatment processin the treatment system 10. Furthermore, the data processor 20 iscoupled to the process controller 12 and the metrology system 14. Thedata processor 20 is capable of interacting with the process controller12 and the metrology system 14 and exchanging data therewith, andcharacterizing the inter-relationships between process data from processcontroller 12 coupled to treatment system 10 and measured metrology datafrom metrology system 14 using multivariate analysis.

In the illustrated embodiment, material processing system 1, depicted inFIG. 1, may comprise a lithography system having a track system coupledto a lithographic exposure system, the combination of which isconfigured to form a film of light-sensitive material, such asphotoresist, on a substrate having a pattern, such as an integratedcircuit pattern, formed thereon. The patterned film may serve as apatterned mask in a subsequent processing step, such as an etching step.In a process for preparing a lithographic structure, the process datamay include, for example, the temperature of the post-application bake(PAB) following the application (or coating) of light-sensitive materialto the substrate, the exposure focus during pattern exposure, theexposure dose during pattern exposure, or the temperature of thepost-exposure bake (PEB) following pattern exposure. Additionally, theprocess data may include other parameters such as dispensing rates andspin rates associated with the (light-sensitive material) coatingprocess prior to PAB, or the developing process following PEB.

Alternatively, material processing system 1 may comprise an etchingsystem. The etching system may include a dry etching system or a wetetching system configured to transfer a pattern formed in a mask layerto an underlying layer or layers. For instance, a dry etching system caninclude a dry plasma etching system configured to facilitate theformation of plasma to assist the creation of chemically reactiveconstituents and catalyze chemical reactions at the substrate surface.In a process for etching a pattern into an underlying layer, the processdata may include, for example, a gas pressure in the treatment system, aflow rate of one or more chemical species (of a process gas) introducedto the treatment system, the power (such as radio frequency (RF) powercoupled to the process gas through an electrode in order to facilitateformation of plasma), a time for performing the etching process, or thesubstrate temperature during processing (which may, in turn, include anelectrostatic clamping voltage applied to electrically clamp thesubstrate to a substrate holder, the temperature of the substrateholder, or a backside pressure of (helium) gas supplied to the backsideof the substrate, or any combination thereof, for example).

In another embodiment, material processing system 1 comprises adielectric coating chamber such as, for example, a spin-on-glass (SOG)or spin-on-dielectric (SOD) system. In another embodiment, materialprocessing system 1 comprises a deposition chamber such as, for example,a chemical vapor deposition (CVD) system, a plasma enhanced CVD (PECVD)system, an atomic layer deposition (ALD) system, a plasma enhanced ALD(PEALD) system, or a physical vapor deposition (PVD) system. In anadditional embodiment, material processing system 1 comprises a rapidthermal processing (RTP) chamber such as, for example, a RTP system forthermal annealing. In another embodiment, material processing system 1comprises a batch diffusion furnace. In yet another embodiment, materialprocessing system 1 can comprise any number of treatment systems foundin a semiconductor device manufacturing facility.

Referring still to FIG. 1, metrology system 14 can include an opticalmetrology system, such as an optical scatterometry system. For instance,the scatterometry system may include an integrated optical digitalprofilometry scatterometry module configured to measure processperformance data resulting from the execution of a treatment process inthe treatment system 10. The metrology system 14 may, for example,measure or monitor metrology data resulting from the treatment process.The metrology data can, for example, be utilized to determine processperformance data that characterizes the treatment process, such as aprocess rate, a relative process rate, a feature profile angle, acritical dimension, a feature thickness or depth, a feature shape, etc.For example, in a process for preparing a lithographic structure,process performance data can include a critical dimension (CD), such asa top, middle or bottom CD in a feature (i.e., via, line, etc.), afeature depth, a sidewall angle, a sidewall shape, a spatialdistribution of any parameter thereof, a parameter to characterize theuniformity of any spatial distribution thereof, etc. Additionally, forexample, in a process for etching a pattern into an underlying layer ona substrate, process performance data can include a critical dimension(CD), such as a top, middle or bottom CD in a feature (i.e., via, line,etc.), a feature depth, a sidewall angle, a sidewall shape, an etchrate, a relative etch rate (e.g., etch selectivity), etc.

The metrology system can be either an in-situ or ex-situ device. Forexample, the metrology system may include a scatterometer, incorporatingbeam profile ellipsometry (ellipsometer) and beam profile reflectometry(reflectometer), which is positioned within the transfer chamber (notshown) to analyze substrates transferred into and out of treatmentsystem 10.

When performing optical metrology, such as scatterometry, a structure tobe examined on a substrate, such as a semiconductor wafer or flat panel,is illuminated with electromagnetic (EM) radiation, and a diffractedsignal received from the structure is utilized to determine the profileof the structure. The structure may include a periodic structure, or anon-periodic structure. Additionally, the structure may include anoperating structure on the substrate (e.g., a via or contact hole, or aninterconnect line or trench, or a feature formed in a mask layerassociated therewith), or the structure may include a periodic gratingor non-periodic grating formed proximate to an operating structureformed on a substrate. In this example, the structure to be examined isa periodic grating and can be formed adjacent a transistor formed on thesubstrate. Alternatively, the periodic grating can be formed in an areaof the transistor that does not interfere with the operation of thetransistor. The profile of the periodic grating is obtained to determinewhether the periodic grating, and by extension the operating structureadjacent the periodic grating, has been fabricated according tospecifications. For instance, FIG. 2 illustrates an exemplary structureon a substrate, such as a silicon substrate, having a top criticaldimension (CD) x₀, a bottom CD x₁, and a height x₂. Additionally, thestructure may reside atop another layer having a thickness x₃, such asan anti-reflective coating (ARC) layer. For example, the structureillustrated in FIG. 2 may represent a lithographic structure.

Referring now to FIG. 3, a periodic grating 52 (or any other type ofstructure to be examined) on a substrate 50 is illuminated by anincident signal 54 from an EM source, such as an ellipsometer orreflectometer. The incident signal 54 is directed onto the periodicgrating 52 at an angle of incidence (θ_(i)) with respect to the surfacenormal vector (n) of the periodic grating 52. A diffraction signal 56leaves the periodic grating 52 at an angle of diffraction (θ_(d)) withrespect to the surface normal vector. In one exemplary embodiment, theangle of incidence is near the Brewster's angle. However, the angle ofincidence can vary depending upon the application. For instance, theangle of incidence can range from approximately 0 degrees toapproximately 90 degrees.

The diffraction signal is received by a detector and analyzed by asignal processing system. When the EM source is an ellipsometer, themagnitude and the phase of the diffraction signal are received anddetected. When the EM source is a reflectometer, the relative intensityof the diffraction signal is received and detected. For instance, FIG. 4illustrates an exemplary diffraction signal obtained using ascatterometric technique.

The signal processing system compares the diffraction signal received bythe detector (i.e., the measured diffraction signal) to simulateddiffraction signals stored in a library of simulated diffraction signalsEach simulated diffraction signal in the library is associated with ahypothetical profile. When a match is made between the measureddiffraction signal and one of the simulated diffraction signals in thelibrary, the hypothetical profile associated with matching simulateddiffraction signal is presumed to represent the actual profile of theperiodic grating or structure. The matching simulated diffraction signaland/or the hypothetical profile can then be provided to assist indetermining whether the periodic grating or structure has beenfabricated according to specifications.

In another embodiment, the signal processing system compares thediffraction signal received by the detector to a series of simulateddiffraction signals determined in real time. The simulated diffractionsignals are determined from an assumed set of profile parameters whereinthe next set of profile parameters are altered according to one or moreoptimization algorithms. For details of the method for generatingsimulated diffraction signals for real time use or to be used in alibrary, refer to U.S. Pat. No. 6,943,900, titled “Generation of alibrary of periodic grating diffraction signals”, which is incorporatedherein in its entirety.

As described above, the library includes simulated diffraction signalsthat are associated with hypothetical profiles of the periodic gratingor structure formed on the substrate of interest. Typically, the processfor preparing the library can include: (1) characterizing the film stackof the periodic grating or structure; (2) obtaining the opticalproperties of the materials used in forming the periodic grating orstructure; (3) obtaining measured diffraction signals from the periodicgrating or structure; (4) determining the number of hypotheticalparameters (e.g., geometrical parameters, which may be related toprocess performance parameters such as CD) to use in modeling theprofile of the periodic grating or structure; (5) adjusting the range tovary the hypothetical parameters in generating a set of hypotheticalprofiles; (6) determining the number of layers to use in dividing up ahypothetical profile to generate a simulated diffraction signal for thehypothetical profile; (7) determining the number of harmonic orders touse in generating the set of simulated diffraction signals; (8)determining a resolution to use in generating the set of simulateddiffraction signals; (9) and generating the set of simulated diffractionsignals based on the adjusted range, parameterization, and/orresolution.

For example, the library can include a range of diffraction signalssufficiently broad to capture the corresponding substrate-to-substratevariations, and batch-to-batch variations, or drift in the set ofhypothetical parameters associated with a pre-determined process ofrecord (or nominal process recipe) for performing the specific substratetreatment process. Additionally, for example, the library can include arange of diffraction signals sufficiently broad to capture thecorresponding variations in the set of hypothetical parametersassociated with a pre-determined process window for performing thespecific substrate treatment process.

However, since the relationship between process data (e.g., values ofprocess variables in the treatment process such temperature and time fora treatment process), metrology data (e.g., measurement values ofmetrology instruments such as scatterometers, CDSEMs, and the like), andprocess performance data (e.g., data characterizing the treatmentprocess, such as a process rate, a relative process rate, a featureprofile angle, a critical dimension, a feature thickness or depth, afeature shape, etc.) are not known a priori, the generation of thelibrary and the determination of a sufficient resolution in generatingthe library is often very labor-intensive and time consuming, even whenthere exists some experience regarding these inter-relationships.Moreover, a separate library is required for each application.

Thus, in one embodiment, multivariate analysis, when applied to two ormore sets of process data, metrology data, and process performance data,can assist in identifying these inter-relationships. For example, themultivariate analysis can include a linear analysis or a nonlinearanalysis. Additionally, for example, the multivariate analysis caninclude Principal Components Analysis (PCA), Independent ComponentAnalysis, Cross Correlation Analysis, Linear Approximation Analysis, andthe like.

In one embodiment, metrology data is collected by obtaining measurementsfrom an actual semiconductor treatment system or from simulations. Inparticular, in the present example, with continuing reference to FIG. 1,one or more process parameters in the process data can be varied whileholding other process parameters constant, metrology data, such asoptical spectra received from the substrate, at the beginning or end ofeach treatment process step (process condition) can be measured orsimulated.

The metrology data, e.g., a diffraction signal comprising lightintensity as a function of wavelength for each set of process data, canbe recorded and stored digitally on data processor 20 as a data matrixX. For example, each row in the matrix X corresponds to a diffractionsignal (light intensity versus wavelength) for a given variation in theprocess data (e.g., a variation in a process parameter). Thus, thedifferent rows of the matrix X correspond to different diffractionsignal for different variations in the process data. Each column in thematrix X corresponds to a specific wavelength in the diffraction signal.Hence, a matrix X assembled from metrology data has the dimensions m byn, where, for example, m is the number of measurements and n is thenumber of wavelengths.

In one exemplary embodiment, statistical data calculations can beperformed on the collected metrology data. For example, the data storedin the matrix X can be mean-centered and/or normalized, if desired.Centering the data stored in a matrix column involves computing the meanvalue of the column elements and subtracting it from each element.Moreover, the data residing in a column of the matrix can be normalizedby the standard deviation of the data in the column. Furthermore, thecentering coefficients and/or normalization coefficients may be updatedfollowing each acquisition of new metrology data; for further details,see U.S. patent application Ser. No. 10/660,697, entitled “Method andsystem of diagnosing a processing system using adaptive multivariateanalysis”; the entire content of which is incorporated herein byreference in its entirety. It should be recognized that the step ofperforming statistical data calculations can be omitted in someapplications.

In one exemplary embodiment, multivariate analysis is used to determinethe extent to which variations in process data contribute to change inthe metrology data (e.g., the spectral signature of each diffractionsignal (optical spectrum)). For example, to determine theinter-relationships between variations in process data and the metrologydata, the matrix X is subject to multivariate analysis.

In one exemplary embodiment, principal components analysis (PCA) isemployed to derive a correlation structure within matrix X byapproximating matrix X with a matrix product ( TP^(T) ) of lowerdimensions plus an error matrix E:X = TP ^(T) + E,  (1)where T is a (m by p) matrix of scores that summarizes the X-variablesand P is a (n by p, where p≦n) matrix of loadings showing the influenceof the variables.

In general, the loadings matrix P can be shown to comprise theeigenvectors of the covariance matrix of X, where the covariance matrixS can be shown to be:S= X ^(T) T   (2)

The covariance matrix S is a real, symmetric matrix and, therefore, itcan be described as:S= UΛU ^(T),  (3)where the real, symmetric eigenvector matrix U comprises the normalizedeigenvectors as columns and Λ is a diagonal matrix comprising theeigenvalues corresponding to each eigenvector along the diagonal.

Using equations (1) and (3) (for a full matrix of p=n; i.e. no errormatrix), the following can be show:P= U  (4)andT ^(T) T= Λ.  (5)

A result of the above eigenanalysis is that each eigenvalue representsthe variance of the metrology data in the direction of the correspondingeigenvector within n-dimensional space. Hence, the largest eigenvaluecorresponds to the greatest variance in the metrology data within then-dimensional space, while the smallest eigenvalue represents thesmallest variance in the metrology data. By definition, all eigenvectorsare orthogonal and, therefore, the second largest eigenvalue correspondsto the second greatest variance in the metrology data in the directionof the corresponding eigenvector which is normal to the direction of thefirst eigenvector.

In one embodiment, one or more essential variables are obtained fromperforming the multivariate analysis. In particular, one or more of theeigenvalues and eigenvectors from the multivariate analysis is selectedas the one or more essential variables. The one or more essentialvariables can then be used to transform newly acquired metrology data toproduce refined metrology data.

In the present example, after performing PCA analysis, the loadingsmatrix P can be utilized to transform new metrology data (e.g., newlyacquired (raw) diffraction signal) into refined metrology data (e.g.,enhanced diffraction signal) by projecting the new metrology data ontothe loadings matrix P (or set of principal components) to produce a setof scores (e.g., refined metrology data or enhanced data signal).

In one embodiment, all of the eigenvectors (or principal components) (n)are utilized in the creation of the loadings matrix P. In an anotherembodiment, a fraction (<n) of the eigenvectors (or principalcomponents) are utilized in the creation of the loadings matrix P. Forexample, the first three to four largest eigenvalues (and correspondingeigenvectors) are chosen to approximate the data and assemble theloadings matrix P. As a result of the approximation, an error E isintroduced to the representation in equation (1).

An example of commercially available software which supports PCAmodeling is MATLAB, or another is SIMCA-P 8.0; for further details, seethe User's Manual (User Guide to SIMCA-P 8.0: A new standard inmultivariate data analysis, Umetrics AB, Version 8.0, September 1999).

While referring to flow chart 500 in FIG. 9, an application example isprovided whereby a treatment process is characterized by defining aprocess window using one or more calculated principal components(hereinafter referred to as essential variables (EV1, EV2, EV3, . . .)). For this example, the treatment process can comprise a process forforming a lithographic structure on a substrate using a treatment systemhaving a track system and an exposure system. As described above, theprocess data in the preparation of a lithographic structure can include,for example, the temperature of the post-application bake (PAB)following the application (or coating) of light-sensitive material tothe substrate, the exposure focus during pattern exposure, the exposuredose during pattern exposure, or the temperature of the post-exposurebake (PEB) following pattern exposure.

While holding two of these process parameters constant (e.g., PABtemperature and PEB temperature), the remaining two process parameters(e.g., exposure focus and dose) are varied over a pre-determinedtwo-dimensional process space. For each process condition, a metrologydata (e.g., a diffraction signal such as the one depicted in FIG. 4) ismeasured and collected as a row in a data matrix ( X) as described above(see 510 in FIG. 9). For instance, as the exposure system steps across asubstrate, the exposure focus or dose is varied. One or more substratesmay be utilized to assemble the data matrix ( X).

Once the data matrix is assembled, the collected data may be optionallysubjected to statistical data calculations (see 520 in FIG. 9). Thecollected data may be mean-centered (e.g., the mean value of thecollected data in a column is subtracted from each element in thecolumn). Additionally, the collected data may be normalized (e.g., thecollected data in a column may be normalized by the mean value of thecollected data in a column or the root mean square (rms) value of thecollected data in a column).

After performing statistical data calculations on the collectedmetrology data (as shown in 530 of FIG. 9), the covariance matrix iscalculated from the data matrix, which may have been subjected tostatistical data calculations. Thereafter, as shown in 540 of FIG. 9,the eigenvalues and corresponding eigenvectors are calculated, and, asshown in 550 of FIG. 9, one or more essential variables are identifiedfrom the eigenanalysis. For instance, FIG. 5 illustrates an exemplaryset of three essential variables (or principal components, oreigenvectors) calculated from a set of metrology data collected for thetreatment process configured to prepare a lithographic structure. In thepresent example, the three essential variables are chosen as the firstthree eigenvectors following the sorting of the eigenvectors byeigenvalue in order from largest to smallest.

As shown in 560 of FIG. 9, the percentage of variability explained byeach essential variable can be determined. FIG. 6 presents thepercentage of variability explained by each of the first four essentialvariables, as well as the cumulative sum of squares of all of thevariables in X explained by the extracted principal component(s) for thefirst four essential variables (or principal components). Thereafter,the accuracy of the determined essential variables may be tested asshown in 570 of FIG. 9.

As described above, multivariate analysis can be applied to two or moresets of process data, metrology data, and process performance data. Inthe examples described above, multivariate analysis was applied toprocess data and metrology data. In the following examples, multivariateanalysis is applied to metrology data and process performance data.

In one embodiment, referring now to FIGS. 7A and 8A, the metrology data(e.g., diffraction signals) obtained for the matrix of runs performed(whereby exposure focus and dose are varied) can be correlated withprocess performance data (e.g., feature CD (at the mid-height of thefeature)). For example, assume measured diffraction signals are obtainedas the metrology data. The measured diffraction signals are matched withsimulated diffraction signals stored in a library of diffraction signals(assembled as described above) to determine CD. FIG. 7A presents(mid-height) CD as a function of exposure focus for each value ofexposure dose, and FIG. 8A presents a contour plot of CD as a functionof both exposure focus and dose. Inspection of FIGS. 7A and 8A indicatesthat there exists a range of both exposure focus and exposure dosewithin which the lithographic structure comprises a finite width. Forinstance, in FIG. 7A, the range of exposure focus is from approximately0.0 to approximately 0.2. In FIG. 8A, this process range (or acceptableprocess window) is highlighted by the shaded ellipse.

Additionally, FIG. 7B presents the score of the third essential variable(i.e., the projection of each diffraction signal (optical spectrum) ontothe third essential variable (principal component)) as a function ofexposure focus for each value of exposure dose. FIG. 8B presents ancontour plot of the score of the third essential variable as a functionof both exposure focus and dose. Inspection of FIGS. 7A, 7B, 8A and 8Bindicates that an essential variable can be used to characterize atreatment process in a treatment system by, for instance, defining aprocess window (or space) for the treatment process in the treatmentsystem. For example, if a mid CD of 20 to 30 nm is acceptable, then therange of focus and dose corresponding to the CD of 20-30 nm isconsidered the process window.

Referring now to FIG. 10, a method of operating a treatment system toperform a treatment process on one or more substrates is described. Themethod is represented by a flow chart 600 beginning in 610 withcollecting metrology data (e.g., optical spectra, such as diffractionsignals), or metrology data and process data for one or more treatmentprocesses or treatment steps.

In 620, objectives are set for the analysis of the treatment process ortreatment processes, and the resultant metrology data. For example, themultivariate analysis can be utilized to prepare a model for determininga process window for the treatment process or processes. Alternatively,for example, the multivariate analysis can be utilized to prepare amodel for use in a process control algorithm for the treatment processor processes. Alternatively yet, for example, the multivariate analysiscan be utilized to prepare a model for use in a process fault detectionalgorithm for the treatment process or processes.

In 630, one or more termination criteria are set for the analysis of themetrology data. The termination criteria can, for example, includesetting a minimum or maximum number of essential variables to be used,or setting one or more statistical parameters for the fraction ofvariance in the metrology data to be explained by the essentialvariables.

In 640, multivariate analysis is performed on a set of the collectedmetrology data. For example, the multivariate analysis can includeprincipal components analysis (PCA). Additionally, for example, thecollected metrology data can comprise a plurality of diffraction signals(or optical spectra acquired from illuminating a structure on the one ormore substrates) from an optical metrology system.

In 650, the determination of the essential variables can be validated.For example, the essential variables may be inspected, as in FIG. 5, andthe ability of the essential variables to explain the variation in themetrology data can be verified, as in FIG. 6.

In 660, the results of the multivariate analysis are checked to ensurethat the pre-selected termination criteria are met. If not, in 695, oneor more of the termination criteria, the analysis objectives, themultivariate analysis (calculation) algorithm, or any of the assumptionsemployed in the analysis can be adjusted.

In 670, one or more of the essential variables is selected for use withfuture metrology data. For example, one or more essential variables canbe utilized to transform old metrology data, new metrology data, or testmetrology data, or a combination thereof into refined metrology data,such as a score resulting from the projection of a diffraction signalonto an essential variable.

This refined metrology data, i.e., a score, can be compared with processperformance data, such as a critical dimension, that is recovered fromthe conventional technique of matching the diffraction signal with alibrary of known signals and profiles. Alternatively, this refinedmetrology data can be compared with process performance data, such ascritical dimension, that is recovered from SEM measurements. In doingso, as depicted in FIGS. 7A, 7B, 8A and 8B, one or more essentialvariables can be selected which produce refined metrology data that bestcorrelates with the process performance data, i.e., the criticaldimension, etc.

The inspection of the data in FIGS. 7A, 7B, 8A and 8B may be performedby an operator skilled in the art of such analysis, or it may beperformed using one or more pattern recognition techniques. For example,the shape of the curve in FIG. 7A (focus v. mid CD) has approximatelythe same pattern as the curve in FIG. 7B (focus v. essential variable3). Thus, essential variable 3 is assumed to correspond to mid CD, andfocus can be correlated to mid CD. Based on this correlation, an inputfocus value can be used in the treatment process to determine the midCD.

During step 670, a calibration between the refined metrology data andthe process performance data can be achieved. The calibration can thenbe used to predict process performance data, such as a criticaldimension.

In yet another embodiment, the calibration (or relationship) betweenrefined metrology data, such as PCA scores, and process performance datacan be determined using partial least-squares (PLS) analysis, classicalleast squares (CLS), inverse least squares (ILS), or the like, or neuralnetworks.

For example, in PLS analysis, a plurality of observations (metrologydata) of diffraction signals (or optical spectra) can be acquired for arange of process performance data, such as critical dimension (CD), thatmay be representative of the typical variations for the specifictreatment process. Each metrology data (such as a diffraction signal)can be transformed into refined metrology data by determining theprojection of each diffraction signal onto a set of pre-determinedessential variables. Then, each array of refined metrology data can bestored as a row of a new data matrix X, and the corresponding processperformance data (e.g., CD, etc.) can be stored as a row in a second newdata matrix Y.

Once the data is assembled into their respective matrices, the followingrelationship can be solved using PLS analysis:XB′= Y,  (7)where X′ represents the m by n matrix described above containing therefined metrology data, B′ represents an n by p (p<n) loading (orcorrelation) matrix, and Y′ represents the m by p matrix containing theprocess performance data.

Once the data matrix X′ and the endpoint signal matrix Y′ are assembled,a relationship designed to best approximate the X′ and Y′ spaces and tomaximize the correlation between X′ and Y′ is established using PLSanalysis.

In the PLS analysis, the matrices X′ and Y′ are decomposed as follows:X′= TP ^(T) + E,  (7a)Y′= UC ^(T) + F,  (7b)U= T+ H,  (7c)where T is a matrix of scores that summarizes the X′ variables, P is amatrix of loadings for matrix X′, U is a matrix of scores thatsummarizes the Y′ variables, C is a matrix of weights expressing thecorrelation between Y′ and T( X′), and E, F and H are matrices ofresiduals. Furthermore, in the PLS analysis, there are additionalloadings W called weights that correlate U and X′, and are used tocalculate T.

In summary, the PLS analysis geometrically corresponds to fitting aline, plane or hyper plane to both the X′ and Y′ data represented aspoints in a multidimensional space, with the objective of wellapproximating the original data tables X′ and Y′, and maximizing thecovariance between the observation positions on the hyper planes.

An example of commercially available software which supports PLSanalysis is MATLAB, or another is SIMCA-P 8.0; for further details, seethe User's Manual (User Guide to SIMCA-P 8.0: A new standard inmultivariate data analysis, Umetrics AB, Version 8.0, September 1999).

In 680, once a PCA model is prepared, i.e., one or more essentialvariables are determined to characterize the treatment process orprocesses, the one or more essential variables are utilized to performone or more of the following: characterization of the treatment processor processes; monitoring of the treatment process or processes;adjusting of the treatment process or processes; automated control ofthe treatment process or processes; or fault detection for the treatmentprocess or processes. For example, during characterization of atreatment process or processes, the one or more selected essentialvariables may be used to define a process window, as illustrated inFIGS. 7A, 7B, 8A and 8B.

Alternatively, for example, the one or more selected essential variablesmay be utilized to predict the change in process performance data fromone substrate to the next, or one batch of substrates to the next, usingmetrology data from the current treatment process and a precedingtreatment process. The change in either metrology data or processperformance data can be correlated with an adjustment to process data(using the multivariate analysis from above). The adjustment to theprocess data, with or without a filter, may be performed in order tocorrect the observed variation or drift in metrology data or processperformance data.

Yet alternatively, for example, the one or more selected essentialvariables may be utilized to predict a fault in a treatment process orprocesses, or it may be utilized to predict a drifting treatment processor processes. The one or more selected essential variables may be usedto transform metrology data into refined metrology data. Statistics,such as the variance or root-mean-square variation, of the set ofrefined metrology data may be used to determine the occurrence of afault or drifting treatment process. For instance, when the refinedmetrology data, or a change in the refined metrology data, or astatistical parameter of the refined metrology data exceeds apre-determined threshold, a fault or drifting process is deemed to haveoccurred.

In 690, the accuracy of the essential variables can be checked andre-checked. The one or more essential variables can be used to transformthe metrology data into refined metrology data, and this refinedmetrology data may or may not be correlated with process performancedata as, for example, described above. The refined metrology data can becompared with old (verified) metrology data, or the predicted processperformance data may be compared with process performance data acquiredby conventional techniques, such as library matching, or real-timesimulation, or SEM data.

Referring now to FIG. 11, a material processing system 1001 comprising adata processing system 1020 is depicted for operating a treatment system1010 via controller 1012 and a metrology system 1014 according to, forexample, the method described above. The controller 1012 is configuredto perform at least one of monitoring, measuring, adjusting, orcontrolling, or a combination of two or more thereof, process data forperforming a treatment process in treatment system 1010. The controller1012 is capable of executing the method of performing the treatmentprocess in the treatment system 1010. The metrology system 1014 isconfigured to measure metrology data from one or more substratesresulting from the treatment process performed in treatment system 1010.

Furthermore, the data processing system 1020 is coupled to thecontroller 1012 and the metrology system 1014. The data processingsystem 1020 is capable of interacting with the controller 1012 and themetrology system 1014 and exchanging data therewith, and characterizingthe inter-relationships between process data from controller 1012coupled to treatment system 1010 and measured metrology data frommetrology system 1014 using multivariate analysis.

Referring still to FIG. 11, data processing system 1020 comprises apre-processor configured to pre-process process data and metrology datafor data processing system 1020. For example, the pre-processor 1022 maycenter and normalize metrology data prior to determination of essentialvariables. Additionally, data processing system 1020 comprises anessential variable processor 1024 configured to exchange data withpre-processor 1022 and determine essential variables using multivariateanalysis. Furthermore, the essential variable processor 1024 may beconfigured to transform metrology data into refined metrology data foruse with a treatment process or processes. A variable analyzer 1030,coupled to the essential variable processor 1024, may be utilized tovalidate the calculated essential variables. Furthermore, a comparator1026, coupled to the essential variable processor 1024, may be used todetermine whether the pre-defined termination criteria have been met,and adjuster 1028 may be configured to adjust one or more of thetermination criteria, the analysis objective, the multivariate analysis(calculation) algorithm, or any of the assumption imposed during theanalysis.

Additionally, pattern recognition software 1032, such as PLS analysis orother analysis techniques, may be utilized to determine a correlationbetween refined metrology data and process performance data, and anessential variable verifier 1034 may be used to check the accuracy, orthe repeatability of the utilization of the one or more essentialvariables to characterize, monitor, adjust, or control the treatmentprocess in the treatment system.

Referring still to FIG. 11, the data processing system 1020 can comprisea microprocessor, a memory, and a digital I/O port capable of generatingcontrol voltages sufficient to communicate and activate inputs of thecontroller 1012 and the metrology system 1014, as well as monitoroutputs from the controller 1012 and metrology system 1014. Moreover,the data processing system 1020 is coupled to and exchanges informationwith treatment system 1010. One example of data processing system 1020is a DELL PRECISION WORKSTATION 610™, available from Dell Corporation,Dallas, Tex. The data processing system 1020 may also be implemented asa general-purpose computer, digital signal process, etc.

However, the data processing system 1020 may be implemented as a generalpurpose computer system that performs a portion or all of themicroprocessor based processing steps of the invention in response to aprocessor executing one or more sequences of one or more instructionscontained in a memory. Such instructions may be read into the controllermemory from another computer readable medium, such as a hard disk or aremovable media drive. One or more processors in a multi-processingarrangement may also be employed as the controller microprocessor toexecute the sequences of instructions contained in main memory. Inalternative embodiments, hard-wired circuitry may be used in place of orin combination with software instructions. Thus, embodiments are notlimited to any specific combination of hardware circuitry and software.

The data processing system 1020 includes at least one computer readablemedium or memory, such as the controller memory, for holdinginstructions programmed according to the teachings of the invention andfor containing data structures, tables, records, or other data that maybe necessary to implement the present invention. Examples of computerreadable media are compact discs, hard disks, floppy disks, tape,magneto-optical disks, PROMs (EPROM, EEPROM, flash EPROM), DRAM, SRAM,SDRAM, or any other magnetic medium, compact discs (e.g., CD-ROM), orany other optical medium, punch cards, paper tape, or other physicalmedium with patterns of holes, a carrier wave (described below), or anyother medium from which a computer can read.

Software for controlling the data processing system 1020, for driving adevice or devices, and/or for enabling the controller to interact with ahuman user can be stored on any one or on a combination of computerreadable media. Such software may include, but is not limited to, devicedrivers, operating systems, development tools, and applicationssoftware. Such computer readable media further includes the computerprogram product for performing all or a portion (if processing isdistributed) of the processing described above.

The computer code devices may be any interpretable or executable codemechanism, including but not limited to scripts, interpretable programs,dynamic link libraries (DLLs), Java classes, and complete executableprograms. Moreover, parts of the processing may be distributed forbetter performance, reliability, and/or cost.

The term “computer readable medium” as used herein refers to any mediumthat participates in providing instructions to the processor of the dataprocessing system 1020 for execution. A computer readable medium maytake many forms, including but not limited to, non-volatile media,volatile media, and transmission media. Non-volatile media includes, forexample, optical, magnetic disks, and magneto-optical disks, such as thehard disk or the removable media drive. Volatile media includes dynamicmemory, such as the main memory. Moreover, various forms of computerreadable media may be involved in carrying out one or more sequences ofone or more instructions to processor of controller for execution. Forexample, the instructions may initially be carried on a magnetic disk ofa remote computer. The remote computer can load the instructionsremotely into a dynamic memory and send the instructions over a networkto the data processing system 1020.

Data processing system 1020 may be locally located relative to thetreatment system 1010, or it may be remotely located relative to thetreatment system 1010 via an internet or intranet. Thus, data processingsystem 1020 can exchange data with the treatment system 1010 using atleast one of a direct connection, an intranet, or the internet. Dataprocessing system 1020 may be coupled to an intranet at a customer site(i.e., a device maker, etc.), or coupled to an intranet at a vendor site(i.e., an equipment manufacturer). Furthermore, another computer (i.e.,controller, server, etc.) can access data processing system 1020 toexchange data via at least one of a direct connection, an intranet, orthe internet.

Although exemplary embodiments have been described, variousmodifications can be made without departing from the spirit and/or scopeof the present invention. Therefore, the present invention should not beconstrued as being limited to the specific forms shown in the drawingsand described above.

1. A method of transforming metrology data from a semiconductortreatment system using multivariate analysis, the method comprising: a)obtaining a set of metrology data measured or simulated for one or moresubstrates treated using the treatment system; b) determining one ormore essential variables for the obtained set of metrology data usingmultivariate analysis; c) obtaining a first metrology data measured orsimulated for one or more substrates treated using the treatment system,wherein the first metrology data is not one of the metrology data in theset of metrology data obtained in a); and d) transforming the firstmetrology data obtained in c) into a second metrology data using the oneor more essential variables determined in b).
 2. The method of claim 1,wherein the set of metrology data includes a set of diffraction signalsmeasured from illuminating a structure on a substrate, and wherein thefirst metrology data is a diffraction signal measured from illuminatinga structure on a substrate.
 3. The method of claim 1, wherein usingmultivariate analysis comprises using a linear or nonlinear analysis. 4.The method of claim 1, wherein b) comprises: calculating one or moreprincipal components from the obtained set of metrology data usingprincipal components analysis.
 5. The method of claim 1, furthercomprising: performing statistical data calculations on the obtained setof metrology data before b).
 6. The method of claim 5, wherein b)comprises: calculating a covariance matrix from the obtained set ofmetrology data; and calculating eigenvalues and correspondingeigenvectors for the covariance matrix, wherein one or more of theeigenvalues and eigenvectors are used as the one or more essentialvariables.
 7. The method of claim 6, wherein performing statistical datacalculations comprises: centering or normalizing the obtained set ofmetrology data.
 8. The method of claim 1, further comprising: verifyinga percentage of variability in the obtained set of metrology dataindicated by the one or more determined essential variables.
 9. Themethod of claim 1, further comprising: when two or more essentialvariables have been determined, selecting at least one essentialvariable based on a percentage of variability indicated by the essentialvariables.
 10. The method of claim 1, wherein d) comprises: selectingone or more of the essential variables determined in b); and projectingthe one or more selected essential variables onto the first metrologydata to produce the second metrology data.
 11. The method of claim 1,further comprising: characterizing a treatment process performed in thetreatment system using the second metrology data.
 12. The method ofclaim 11, wherein characterizing a treatment process comprises: defininga process window for the treatment process.
 13. The method of claim 11,further comprising: monitoring or controlling the treatment processusing the second metrology data.
 14. The method of claim 1, furthercomprising: before a), collecting the set of metrology data for atreatment process performed in the treatment system; before b),selecting objectives for an analysis of the treatment process; beforeb), selecting one or more termination criteria for performing theanalysis; after b), validating the one or more essential variablesdetermined in b) by computing one or more statistics associated withexplaining the set of metrology data by the one or more essentialvariables; after b), determining if the one or more termination criteriaare met; if the one or more termination criteria are not met, adjustingone or more of the following: the one or more termination criteria, theobjectives for the analysis, or the multivariate analysis; after b),identifying at least one of the one or more essential variablesdetermined in b) using one or more pattern recognition techniques; andutilizing the identified essential variables to characterize, adjust,monitor, or control the treatment process.
 15. The method of claim 14,wherein utilizing the identified essential variables comprises:determining a relationship between the second metrology data and processperformance data related to the profile of one or more structure on oneor more substrates.
 16. A computer-readable medium containing computerexecutable instructions for causing a computer to transform metrologydata from a semiconductor treatment system using multivariate analysis,comprising instructions for: a) obtaining a set of metrology datameasured or simulated for one or more substrates treated using thetreatment system; b) determining one or more essential variables for theobtained set of metrology data using multivariate analysis; c) obtaininga first metrology data measured or simulated for one or more substratestreated using the treatment system, wherein the first metrology data isnot one of the metrology data in the set of metrology data obtained ina); and d) transforming the first metrology data obtained in c) into asecond metrology data using the one or more essential variablesdetermined in b).
 17. The computer-readable medium of claim 16, whereinthe set of metrology data includes a set of diffraction signals measuredfrom illuminating a structure on a substrate, and wherein the firstmetrology data is a diffraction signal measured from illuminating astructure on a substrate.
 18. The computer-readable medium of claim 16,further comprising instructions for: performing statistical datacalculations on the obtained set of metrology data before b).
 19. Thecomputer-readable medium of claim 18, wherein b) comprises instructionsfor: calculating a covariance matrix from the obtained set of metrologydata; and calculating eigenvalues and corresponding eigenvectors for thecovariance matrix, wherein one or more of the eigenvalues andeigenvectors are used as the one or more essential variables.
 20. Thecomputer-readable medium of claim 16, further comprising instructionsfor: when two or more essential variables have been determined,selecting at least one essential variable based on a percentage ofvariability indicated by the essential variables.
 21. Thecomputer-readable medium of claim 16, wherein d) comprises instructionsfor: selecting one or more of the essential variables determined in b);and projecting the one or more selected essential variables onto thefirst metrology data to produce the second metrology data.
 22. Thecomputer-readable medium of claim 16, further comprising instructionsfor: before a), collecting the set of metrology data for a treatmentprocess performed in the treatment system; before b), selectingobjectives for an analysis of the treatment process; before b),selecting one or more termination criteria for performing the analysis;after b), validating the one or more essential variables determined inb) by computing one or more statistics associated with explaining theset of metrology data by the one or more essential variables; after b),determining if the one or more termination criteria are met; if the oneor more termination criteria are not met, adjusting one or more of thefollowing: the one or more termination criteria, the objectives for theanalysis, or the multivariate analysis; after b), identifying at leastone of the one or more essential variables determined in b) using one ormore pattern recognition techniques; and utilizing the identifiedessential variables to characterize, adjust, monitor, or control thetreatment process.
 23. The computer-readable medium of claim 22, whereinutilizing the identified essential variables comprises: determining arelationship between the second metrology data and process performancedata related to the profile of one or more structure on one or moresubstrates.
 24. A system to transform metrology data from asemiconductor treatment system using multivariate analysis, the systemcomprising: a metrology system to measure a set of metrology data forone or more substrates treated using the treatment system; and a dataprocessing system configured to: a) obtain the set of metrology data; b)determine one or more essential variables for the obtained set ofmetrology data using multivariate analysis; c) obtain a first metrologydata measured using the metrology system for one or more substratestreated using the treatment system, wherein the first metrology data isnot one of the metrology data in the set of metrology data obtained ina); and d) transform the first metrology data obtained in c) into asecond metrology data using the one or more essential variablesdetermined in b).
 25. The system of claim 24, wherein the metrologysystem includes an ellipsometer or reflectometer, wherein the set ofmetrology data includes a set of diffraction signals measured fromilluminating a structure on a substrate using the ellipsometer orreflectometer, and wherein the first metrology data is a diffractionsignal measured from illuminating a structure on a substrate using theellipsometer or reflectometer.